LMFDB - Embedded newform 950.2.u.g.99.1

Newspace parameters

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.1
Character	$\chi$	$=$	950.99
Dual form			950.2.u.g.499.1

$q$-expansion

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(-3.16698 + 0.558424i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.558424 - 3.16698i) q^{6} +(0.0202608 + 0.0116976i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.89886 - 2.51098i) q^{9} +O(q^{10})$	\(q+(-0.342020 + 0.939693i) q^{2} +(-3.16698 + 0.558424i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.558424 - 3.16698i) q^{6} +(0.0202608 + 0.0116976i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.89886 - 2.51098i) q^{9} +(-1.08041 - 1.87132i) q^{11} +(2.78500 + 1.60792i) q^{12} +(1.56613 + 0.276152i) q^{13} +(-0.0179217 + 0.0150381i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-2.72922 + 7.49847i) q^{17} +7.34161i q^{18} +(-1.06458 + 4.22690i) q^{19} +(-0.0706976 - 0.0257318i) q^{21} +(2.12799 - 0.375222i) q^{22} +(2.88011 - 3.43239i) q^{23} +(-2.46347 + 2.06710i) q^{24} +(-0.795147 + 1.37724i) q^{26} +(-12.0914 + 6.98095i) q^{27} +(-0.00800160 - 0.0219842i) q^{28} +(7.09702 - 2.58310i) q^{29} +(-2.22993 + 3.86236i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(4.46663 + 5.32312i) q^{33} +(-6.11281 - 5.12925i) q^{34} +(-6.89886 - 2.51098i) q^{36} -0.389132i q^{37} +(-3.60788 - 2.44606i) q^{38} -5.11413 q^{39} +(0.972920 + 5.51771i) q^{41} +(0.0483600 - 0.0576332i) q^{42} +(-6.23734 - 7.43337i) q^{43} +(-0.375222 + 2.12799i) q^{44} +(2.24033 + 3.88037i) q^{46} +(-1.46211 - 4.01711i) q^{47} +(-1.09988 - 3.02190i) q^{48} +(-3.49973 - 6.06170i) q^{49} +(4.45606 - 25.2716i) q^{51} +(-1.02222 - 1.21824i) q^{52} +(-2.43113 + 2.89731i) q^{53} +(-2.42446 - 13.7498i) q^{54} +0.0233951 q^{56} +(1.01111 - 13.9810i) q^{57} +7.55249i q^{58} +(-3.41426 - 1.24269i) q^{59} +(-8.84152 - 7.41891i) q^{61} +(-2.86675 - 3.41646i) q^{62} +(0.169148 + 0.0298254i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.52977 + 2.37664i) q^{66} +(-1.31913 - 3.62429i) q^{67} +(6.91062 - 3.98985i) q^{68} +(-7.20454 + 12.4786i) q^{69} +(-9.85813 + 8.27195i) q^{71} +(4.71909 - 5.62400i) q^{72} +(-1.87269 + 0.330206i) q^{73} +(0.365664 + 0.133091i) q^{74} +(3.53251 - 2.55369i) q^{76} -0.0505526i q^{77} +(1.74914 - 4.80571i) q^{78} +(1.65165 + 9.36698i) q^{79} +(17.5228 - 14.7034i) q^{81} +(-5.51771 - 0.972920i) q^{82} +(-2.27622 - 1.31417i) q^{83} +(0.0376174 + 0.0651553i) q^{84} +(9.11838 - 3.31882i) q^{86} +(-21.0337 + 12.1438i) q^{87} +(-1.87132 - 1.08041i) q^{88} +(-1.54115 + 8.74032i) q^{89} +(0.0285008 + 0.0239150i) q^{91} +(-4.41259 + 0.778059i) q^{92} +(4.90532 - 13.4773i) q^{93} +4.27492 q^{94} +3.21584 q^{96} +(3.81486 - 10.4812i) q^{97} +(6.89312 - 1.21544i) q^{98} +(-12.1524 - 10.1971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36q + 36q^{9} + O(q^{10}) $	$ 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	−3.16698	+	0.558424i	−1.82846	+	0.322406i	−0.978783	−	0.204901i	$-0.934313\pi$
$3$	−3.16698	+	0.558424i	−1.82846	+	0.322406i	−0.849675	+	0.527307i	$0.823202\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	0.558424	−	3.16698i	0.227976	−	1.29291i
$7$	0.0202608	+	0.0116976i	0.00765785	+	0.00442126i	0.503824	−	0.863806i	$-0.331926\pi$
$7$	0.0202608	+	0.0116976i	0.00765785	+	0.00442126i	−0.496166	+	0.868228i	$0.665259\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	6.89886	−	2.51098i	2.29962	−	0.836993i
$10$		0			0
$11$	−1.08041	−	1.87132i	−0.325755	−	0.564225i	0.655910	−	0.754839i	$-0.272285\pi$
$11$	−1.08041	−	1.87132i	−0.325755	−	0.564225i	−0.981665	+	0.190615i	$0.938952\pi$
$12$	2.78500	+	1.60792i	0.803959	+	0.464166i
$13$	1.56613	+	0.276152i	0.434368	+	0.0765907i	0.386557	−	0.922266i	$-0.373664\pi$
$13$	1.56613	+	0.276152i	0.434368	+	0.0765907i	0.0478110	+	0.998856i	$0.484775\pi$
$14$	−0.0179217	+	0.0150381i	−0.00478977	+	0.00401910i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.72922	+	7.49847i	−0.661933	+	1.81865i	−0.0939966	+	0.995573i	$0.529964\pi$
$17$	−2.72922	+	7.49847i	−0.661933	+	1.81865i	−0.567936	+	0.823073i	$0.692258\pi$
$18$			7.34161i			1.73043i
$19$	−1.06458	+	4.22690i	−0.244232	+	0.969717i
$19$	−1.06458	+	4.22690i	−0.244232	+	0.969717i
$20$		0			0
$21$	−0.0706976	−	0.0257318i	−0.0154275	−	0.00561515i
$22$	2.12799	−	0.375222i	0.453689	−	0.0799976i
$23$	2.88011	−	3.43239i	0.600545	−	0.715702i	−0.377050	−	0.926193i	$-0.623062\pi$
$23$	2.88011	−	3.43239i	0.600545	−	0.715702i	0.977596	+	0.210491i	$0.0675061\pi$
$24$	−2.46347	+	2.06710i	−0.502855	+	0.421945i
$25$		0			0
$26$	−0.795147	+	1.37724i	−0.155941	+	0.270098i
$27$	−12.0914	+	6.98095i	−2.32698	+	1.34348i
$28$	−0.00800160	−	0.0219842i	−0.00151216	−	0.00415463i
$29$	7.09702	−	2.58310i	1.31788	−	0.479670i	0.415104	−	0.909774i	$-0.363745\pi$
$29$	7.09702	−	2.58310i	1.31788	−	0.479670i	0.902780	+	0.430104i	$0.141523\pi$
$30$		0			0
$31$	−2.22993	+	3.86236i	−0.400508	+	0.693700i	−0.993787	−	0.111297i	$-0.964500\pi$
$31$	−2.22993	+	3.86236i	−0.400508	+	0.693700i	0.593279	+	0.804997i	$0.297833\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	4.46663	+	5.32312i	0.777540	+	0.926636i
$34$	−6.11281	−	5.12925i	−1.04834	−	0.879660i
$35$		0			0
$36$	−6.89886	−	2.51098i	−1.14981	−	0.418496i
$37$		−	0.389132i		−	0.0639729i	−0.999488	−	0.0319864i	$-0.989817\pi$
$37$		−	0.389132i		−	0.0639729i	0.999488	−	0.0319864i	$-0.0101833\pi$
$38$	−3.60788	−	2.44606i	−0.585275	−	0.396804i
$39$	−5.11413			−0.818916
$40$		0			0
$41$	0.972920	+	5.51771i	0.151945	+	0.861721i	0.961526	+	0.274713i	$0.0885830\pi$
$41$	0.972920	+	5.51771i	0.151945	+	0.861721i	−0.809582	+	0.587007i	$0.800306\pi$
$42$	0.0483600	−	0.0576332i	0.00746212	−	0.00889300i
$43$	−6.23734	−	7.43337i	−0.951185	−	1.13358i	−0.990931	−	0.134369i	$-0.957099\pi$
$43$	−6.23734	−	7.43337i	−0.951185	−	1.13358i	0.0397459	−	0.999210i	$-0.487345\pi$
$44$	−0.375222	+	2.12799i	−0.0565668	+	0.320806i
$45$		0			0
$46$	2.24033	+	3.88037i	0.330319	+	0.572129i
$47$	−1.46211	−	4.01711i	−0.213271	−	0.585956i	0.786218	−	0.617950i	$-0.212037\pi$
$47$	−1.46211	−	4.01711i	−0.213271	−	0.585956i	−0.999488	+	0.0319938i	$0.989814\pi$
$48$	−1.09988	−	3.02190i	−0.158754	−	0.436173i
$49$	−3.49973	−	6.06170i	−0.499961	−	0.865958i
$50$		0			0
$51$	4.45606	−	25.2716i	0.623973	−	3.53873i
$52$	−1.02222	−	1.21824i	−0.141757	−	0.168939i
$53$	−2.43113	+	2.89731i	−0.333941	+	0.397976i	−0.906719	−	0.421735i	$-0.861421\pi$
$53$	−2.43113	+	2.89731i	−0.333941	+	0.397976i	0.572778	+	0.819711i	$0.305866\pi$
$54$	−2.42446	−	13.7498i	−0.329927	−	1.87111i
$55$		0			0
$56$	0.0233951			0.00312630
$57$	1.01111	−	13.9810i	0.133925	−	1.85183i
$58$			7.55249i			0.991691i
$59$	−3.41426	−	1.24269i	−0.444499	−	0.161784i	0.110067	−	0.993924i	$-0.464893\pi$
$59$	−3.41426	−	1.24269i	−0.444499	−	0.161784i	−0.554566	+	0.832140i	$0.687116\pi$
$60$		0			0
$61$	−8.84152	−	7.41891i	−1.13204	−	0.949894i	−0.132891	−	0.991131i	$-0.542426\pi$
$61$	−8.84152	−	7.41891i	−1.13204	−	0.949894i	−0.999149	+	0.0412364i	$0.986870\pi$
$62$	−2.86675	−	3.41646i	−0.364077	−	0.433890i
$63$	0.169148	+	0.0298254i	0.0213107	+	0.00375765i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−6.52977	+	2.37664i	−0.803759	+	0.292544i
$67$	−1.31913	−	3.62429i	−0.161158	−	0.442778i	0.832662	−	0.553781i	$-0.186816\pi$
$67$	−1.31913	−	3.62429i	−0.161158	−	0.442778i	−0.993820	+	0.111004i	$0.964593\pi$
$68$	6.91062	−	3.98985i	0.838036	−	0.483840i
$69$	−7.20454	+	12.4786i	−0.867325	+	1.50225i
$70$		0			0
$71$	−9.85813	+	8.27195i	−1.16994	+	0.981700i	−0.999993	−	0.00375214i	$-0.998806\pi$
$71$	−9.85813	+	8.27195i	−1.16994	+	0.981700i	−0.169952	+	0.985452i	$0.554361\pi$
$72$	4.71909	−	5.62400i	0.556151	−	0.662795i
$73$	−1.87269	+	0.330206i	−0.219182	+	0.0386477i	−0.282161	−	0.959367i	$-0.591051\pi$
$73$	−1.87269	+	0.330206i	−0.219182	+	0.0386477i	0.0629785	+	0.998015i	$0.479940\pi$
$74$	0.365664	+	0.133091i	0.0425076	+	0.0154715i
$75$		0			0
$76$	3.53251	−	2.55369i	0.405207	−	0.292928i
$77$		−	0.0505526i		−	0.00576100i
$78$	1.74914	−	4.80571i	0.198051	−	0.544139i
$79$	1.65165	+	9.36698i	0.185825	+	1.05387i	0.924891	+	0.380233i	$0.124156\pi$
$79$	1.65165	+	9.36698i	0.185825	+	1.05387i	−0.739065	+	0.673634i	$0.764733\pi$
$80$		0			0
$81$	17.5228	−	14.7034i	1.94698	−	1.63371i
$82$	−5.51771	−	0.972920i	−0.609329	−	0.107441i
$83$	−2.27622	−	1.31417i	−0.249847	−	0.144249i	0.369847	−	0.929093i	$-0.379410\pi$
$83$	−2.27622	−	1.31417i	−0.249847	−	0.144249i	−0.619694	+	0.784843i	$0.712743\pi$
$84$	0.0376174	+	0.0651553i	0.00410440	+	0.00710903i
$85$		0			0
$86$	9.11838	−	3.31882i	0.983260	−	0.357877i
$87$	−21.0337	+	12.1438i	−2.25505	+	1.30195i
$88$	−1.87132	−	1.08041i	−0.199484	−	0.115172i
$89$	−1.54115	+	8.74032i	−0.163362	+	0.926472i	0.787375	+	0.616474i	$0.211439\pi$
$89$	−1.54115	+	8.74032i	−0.163362	+	0.926472i	−0.950737	+	0.309998i	$0.899672\pi$
$90$		0			0
$91$	0.0285008	+	0.0239150i	0.00298769	+	0.00250697i
$92$	−4.41259	+	0.778059i	−0.460045	+	0.0811183i
$93$	4.90532	−	13.4773i	0.508658	−	1.39753i
$94$	4.27492			0.440924
$95$		0			0
$96$	3.21584			0.328215
$97$	3.81486	−	10.4812i	0.387340	−	1.06421i	−0.580854	−	0.814008i	$-0.697281\pi$
$97$	3.81486	−	10.4812i	0.387340	−	1.06421i	0.968194	−	0.250201i	$-0.0804966\pi$
$98$	6.89312	−	1.21544i	0.696310	−	0.122778i
$99$	−12.1524	−	10.1971i	−1.22137	−	1.02485i
$100$		0			0
$101$	−3.23809	+	18.3641i	−0.322202	+	1.82730i	0.206449	+	0.978457i	$0.433809\pi$
$101$	−3.23809	+	18.3641i	−0.322202	+	1.82730i	−0.528651	+	0.848840i	$0.677302\pi$
$102$	22.2234	+	12.8307i	2.20045	+	1.27043i
$103$	−3.06218	+	1.76795i	−0.301726	+	0.174201i	−0.643218	−	0.765683i	$-0.722401\pi$
$103$	−3.06218	+	1.76795i	−0.301726	+	0.174201i	0.341492	+	0.939885i	$0.389068\pi$
$104$	1.49439	−	0.543913i	0.146537	−	0.0533350i
$105$		0			0
$106$	−1.89108	−	3.27545i	−0.183678	−	0.318140i
$107$	−4.84336	−	2.79632i	−0.468226	−	0.270330i	0.247271	−	0.968946i	$-0.420466\pi$
$107$	−4.84336	−	2.79632i	−0.468226	−	0.270330i	−0.715497	+	0.698616i	$0.753800\pi$
$108$	13.7498	+	2.42446i	1.32307	+	0.233294i
$109$	−7.21936	+	6.05777i	−0.691490	+	0.580229i	−0.919338	−	0.393468i	$-0.871275\pi$
$109$	−7.21936	+	6.05777i	−0.691490	+	0.580229i	0.227849	+	0.973697i	$0.426831\pi$
$110$		0			0
$111$	0.217301	+	1.23237i	0.0206253	+	0.116972i
$112$	−0.00800160	+	0.0219842i	−0.000756080	+	0.00207731i
$113$			5.69339i			0.535589i	0.963476	+	0.267795i	$0.0862948\pi$
$113$			5.69339i			0.535589i	−0.963476	+	0.267795i	$0.913705\pi$
$114$	12.7920	+	5.73191i	1.19808	+	0.536843i
$115$		0			0
$116$	−7.09702	−	2.58310i	−0.658942	−	0.239835i
$117$	11.4979	−	2.02740i	1.06299	−	0.187433i
$118$	2.33549	−	2.78333i	0.214999	−	0.256226i
$119$	−0.143010	+	0.119999i	−0.0131097	+	0.0110003i
$120$		0			0
$121$	3.16544	−	5.48269i	0.287767	−	0.498427i
$122$	9.99547	−	5.77089i	0.904948	−	0.522472i
$123$	−6.16244	−	16.9312i	−0.555649	−	1.52663i
$124$	4.19091	−	1.52536i	0.376354	−	0.136982i
$125$		0			0
$126$	−0.0858789	+	0.148747i	−0.00765070	+	0.0132514i
$127$	8.54334	+	1.50642i	0.758099	+	0.133673i	0.539320	−	0.842101i	$-0.318681\pi$
$127$	8.54334	+	1.50642i	0.758099	+	0.133673i	0.218779	+	0.975774i	$0.429793\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	23.9045	+	20.0583i	2.10468	+	1.76603i
$130$		0			0
$131$	−19.4945	−	7.09542i	−1.70324	−	0.619930i	−0.707055	−	0.707159i	$-0.749977\pi$
$131$	−19.4945	−	7.09542i	−1.70324	−	0.619930i	−0.996188	+	0.0872292i	$0.972199\pi$
$132$		−	6.94884i		−	0.604818i
$133$	−0.0710136	+	0.0731872i	−0.00615766	+	0.00634613i
$134$	3.85689			0.333185
$135$		0			0
$136$	1.38566	+	7.85847i	0.118819	+	0.673858i
$137$	−3.83636	+	4.57200i	−0.327762	+	0.390612i	−0.904610	−	0.426240i	$-0.859838\pi$
$137$	−3.83636	+	4.57200i	−0.327762	+	0.390612i	0.576848	+	0.816852i	$0.304283\pi$
$138$	−9.26198	−	11.0380i	−0.788432	−	0.939617i
$139$	2.44517	−	13.8672i	0.207397	−	1.17620i	−0.686227	−	0.727387i	$-0.740734\pi$
$139$	2.44517	−	13.8672i	0.207397	−	1.17620i	0.893624	−	0.448817i	$-0.148155\pi$
$140$		0			0
$141$	6.87373	+	11.9056i	0.578872	+	1.00264i
$142$	−4.40141	−	12.0928i	−0.369358	−	1.01480i
$143$	−1.17530	−	3.22910i	−0.0982832	−	0.270031i
$144$	3.67080	+	6.35802i	0.305900	+	0.529835i
$145$		0			0
$146$	0.330206	−	1.87269i	0.0273281	−	0.154985i
$147$	14.4686	+	17.2430i	1.19335	+	1.42218i
$148$	−0.250129	+	0.298092i	−0.0205605	+	0.0245030i
$149$	−1.22145	−	6.92721i	−0.100065	−	0.567499i	−0.993077	−	0.117465i	$-0.962523\pi$
$149$	−1.22145	−	6.92721i	−0.100065	−	0.567499i	0.893012	−	0.450034i	$-0.148588\pi$
$150$		0			0
$151$	−14.0840			−1.14614			−0.573070	−	0.819507i	$-0.694248\pi$
$151$	−14.0840			−1.14614			−0.573070	+	0.819507i	$0.694248\pi$
$152$	1.19149	+	4.19289i	0.0966429	+	0.340088i
$153$			58.5838i			4.73622i
$154$	0.0475039	+	0.0172900i	0.00382797	+	0.00139327i
$155$		0			0
$156$	3.91765	+	3.28730i	0.313663	+	0.263195i
$157$	1.74085	+	2.07466i	0.138935	+	0.165576i	0.831025	−	0.556235i	$-0.187755\pi$
$157$	1.74085	+	2.07466i	0.138935	+	0.165576i	−0.692090	+	0.721811i	$0.743310\pi$
$158$	−9.36698	−	1.65165i	−0.745197	−	0.131398i
$159$	6.08141	−	10.5333i	0.482288	−	0.835346i
$160$		0			0
$161$	0.0985039	−	0.0358525i	0.00776319	−	0.00282557i
$162$	7.82350	+	21.4949i	0.614672	+	1.68880i
$163$	−11.9479	+	6.89810i	−0.935829	+	0.540301i	−0.888650	−	0.458585i	$-0.848356\pi$
$163$	−11.9479	+	6.89810i	−0.935829	+	0.540301i	−0.0471785	+	0.998886i	$0.515023\pi$
$164$	2.80141	−	4.85219i	0.218754	−	0.378892i
$165$		0			0
$166$	2.01343	−	1.68947i	0.156273	−	0.131128i
$167$	−15.5969	+	18.5877i	−1.20692	+	1.43836i	−0.339632	+	0.940558i	$0.610302\pi$
$167$	−15.5969	+	18.5877i	−1.20692	+	1.43836i	−0.867293	+	0.497798i	$0.834142\pi$
$168$	−0.0740919	+	0.0130644i	−0.00571631	+	0.00100794i
$169$	−9.83949	−	3.58128i	−0.756884	−	0.275483i
$170$		0			0
$171$	3.26925	+	31.8339i	0.250006	+	2.43440i
$172$			9.70358i			0.739891i
$173$	6.62267	−	18.1956i	0.503512	−	1.38339i	−0.384311	−	0.923204i	$-0.625561\pi$
$173$	6.62267	−	18.1956i	0.503512	−	1.38339i	0.887823	−	0.460184i	$-0.152217\pi$
$174$	−4.21749	−	23.9186i	−0.319727	−	1.81326i
$175$		0			0
$176$	1.65528	−	1.38895i	0.124772	−	0.104696i
$177$	11.5068	+	2.02897i	0.864907	+	0.152506i
$178$	−7.68611	−	4.43758i	−0.576098	−	0.332610i
$179$	4.29621	+	7.44125i	0.321114	+	0.556185i	0.980718	−	0.195428i	$-0.0626095\pi$
$179$	4.29621	+	7.44125i	0.321114	+	0.556185i	−0.659604	+	0.751613i	$0.729276\pi$
$180$		0			0
$181$	3.94197	−	1.43476i	0.293005	−	0.106645i	−0.191336	−	0.981525i	$-0.561282\pi$
$181$	3.94197	−	1.43476i	0.293005	−	0.106645i	0.484340	+	0.874880i	$0.339060\pi$
$182$	−0.0322206	+	0.0186026i	−0.00238835	+	0.00137891i
$183$	32.1438	+	18.5582i	2.37614	+	1.37186i
$184$	0.778059	−	4.41259i	0.0573593	−	0.325301i
$185$		0			0
$186$	10.9868	+	9.21899i	0.805589	+	0.675969i
$187$	16.9807	−	2.99416i	1.24175	−	0.218955i
$188$	−1.46211	+	4.01711i	−0.106635	+	0.292978i
$189$	−0.326640			−0.0237596
$190$		0			0
$191$	18.8620			1.36481			0.682403	−	0.730976i	$-0.260935\pi$
$191$	18.8620			1.36481			0.682403	+	0.730976i	$0.260935\pi$
$192$	−1.09988	+	3.02190i	−0.0793771	+	0.218087i
$193$	−17.5242	+	3.08999i	−1.26142	+	0.222422i	−0.764073	−	0.645130i	$-0.776803\pi$
$193$	−17.5242	+	3.08999i	−1.26142	+	0.222422i	−0.497346	+	0.867552i	$0.665692\pi$
$194$	8.54438	+	7.16959i	0.613451	+	0.514747i
$195$		0			0
$196$	−1.21544	+	6.89312i	−0.0868173	+	0.492365i
$197$	−11.7025	−	6.75642i	−0.833766	−	0.481375i	0.0213742	−	0.999772i	$-0.493196\pi$
$197$	−11.7025	−	6.75642i	−0.833766	−	0.481375i	−0.855140	+	0.518396i	$0.826529\pi$
$198$	13.7385	−	7.93194i	0.976354	−	0.563698i
$199$	6.59301	−	2.39966i	0.467366	−	0.170107i	−0.0975926	−	0.995226i	$-0.531114\pi$
$199$	6.59301	−	2.39966i	0.467366	−	0.170107i	0.564959	+	0.825119i	$0.308892\pi$
$200$		0			0
$201$	6.20156	+	10.7414i	0.437425	+	0.757642i
$202$	−16.1491	−	9.32370i	−1.13625	−	0.656013i
$203$	0.174007	+	0.0306821i	0.0122129	+	0.00215346i
$204$	−19.6578	+	16.4948i	−1.37632	+	1.15487i
$205$		0			0
$206$	−0.614003	−	3.48218i	−0.0427796	−	0.242615i
$207$	11.2508	−	30.9114i	0.781988	−	2.14849i
$208$			1.59029i			0.110267i
$209$	9.06007	−	2.57460i	0.626698	−	0.178089i
$210$		0			0
$211$	−6.68827	−	2.43433i	−0.460440	−	0.167586i	0.101377	−	0.994848i	$-0.467675\pi$
$211$	−6.68827	−	2.43433i	−0.460440	−	0.167586i	−0.561817	+	0.827262i	$0.689897\pi$
$212$	3.72471	−	0.656766i	0.255814	−	0.0451069i
$213$	26.6013	−	31.7021i	1.82269	−	2.17219i
$214$	4.28421	−	3.59488i	0.292862	−	0.245741i
$215$		0			0
$216$	−6.98095	+	12.0914i	−0.474994	+	0.822713i
$217$	−0.0903603	+	0.0521696i	−0.00613406	+	0.00354150i
$218$	−3.22327	−	8.85586i	−0.218307	−	0.599795i
$219$	5.74639	−	2.09151i	0.388305	−	0.141331i
$220$		0			0
$221$	−6.34504	+	10.9899i	−0.426813	+	0.739263i
$222$	−1.23237	−	0.217301i	−0.0827115	−	0.0145843i
$223$	2.80259	+	3.34000i	0.187675	+	0.223663i	0.851675	−	0.524070i	$-0.175587\pi$
$223$	2.80259	+	3.34000i	0.187675	+	0.223663i	−0.664000	+	0.747733i	$0.731142\pi$
$224$	−0.0179217	−	0.0150381i	−0.00119744	−	0.00100477i
$225$		0			0
$226$	−5.35004	−	1.94725i	−0.355879	−	0.129529i
$227$			9.44623i			0.626969i	0.949593	+	0.313484i	$0.101496\pi$
$227$			9.44623i			0.626969i	−0.949593	+	0.313484i	$0.898504\pi$
$228$	−9.76136	+	10.0601i	−0.646462	+	0.666249i
$229$	−22.8675			−1.51112			−0.755562	−	0.655077i	$-0.772636\pi$
$229$	−22.8675			−1.51112			−0.755562	+	0.655077i	$0.772636\pi$
$230$		0			0
$231$	0.0282298	+	0.160099i	0.00185738	+	0.0105337i
$232$	4.85465	−	5.78554i	0.318723	−	0.379840i
$233$	6.79851	+	8.10215i	0.445385	+	0.530790i	0.941295	−	0.337584i	$-0.109610\pi$
$233$	6.79851	+	8.10215i	0.445385	+	0.530790i	−0.495910	+	0.868374i	$0.665165\pi$
$234$	−2.02740	+	11.4979i	−0.132535	+	0.751644i
$235$		0			0
$236$	1.81669	+	3.14660i	0.118256	+	0.204826i
$237$	−10.4615	−	28.7427i	−0.679547	−	1.86704i
$238$	−0.0638504	−	0.175427i	−0.00413880	−	0.0113713i
$239$	8.67636	+	15.0279i	0.561227	+	0.972074i	0.997390	+	0.0722058i	$0.0230038\pi$
$239$	8.67636	+	15.0279i	0.561227	+	0.972074i	−0.436163	+	0.899868i	$0.643663\pi$
$240$		0			0
$241$	−0.0833347	+	0.472614i	−0.00536806	+	0.0304438i	−0.987374	−	0.158406i	$-0.949365\pi$
$241$	−0.0833347	+	0.472614i	−0.00536806	+	0.0304438i	0.982006	+	0.188849i	$0.0604758\pi$
$242$	4.06940	+	4.84973i	0.261591	+	0.311752i
$243$	−20.3600	+	24.2641i	−1.30610	+	1.55655i
$244$	2.00421	+	11.3664i	0.128306	+	0.727661i
$245$		0			0
$246$	18.0178			1.14877
$247$	−2.83454	+	6.32590i	−0.180358	+	0.402508i
$248$			4.45987i			0.283202i
$249$	7.94260	+	2.89087i	0.503342	+	0.183202i
$250$		0			0
$251$	4.56913	+	3.83396i	0.288401	+	0.241997i	0.775497	−	0.631351i	$-0.217499\pi$
$251$	4.56913	+	3.83396i	0.288401	+	0.241997i	−0.487096	+	0.873348i	$0.661944\pi$
$252$	−0.110404	−	0.131574i	−0.00695478	−	0.00828839i
$253$	−9.53480	−	1.68124i	−0.599448	−	0.105699i
$254$	−4.33757	+	7.51289i	−0.272163	+	0.471400i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	4.62683	+	12.7121i	0.288614	+	0.792959i	0.996261	+	0.0863936i	$0.0275343\pi$
$257$	4.62683	+	12.7121i	0.288614	+	0.792959i	−0.707648	+	0.706566i	$0.750244\pi$
$258$	−27.0244	+	15.6026i	−1.68247	+	0.971373i
$259$	0.00455189	−	0.00788411i	0.000282841	−	0.000489895i
$260$		0			0
$261$	42.4752	−	35.6409i	2.62915	−	2.20612i
$262$	13.3350	−	15.8921i	0.823841	−	0.981815i
$263$	−17.3493	+	3.05915i	−1.06980	+	0.188635i	−0.680703	−	0.732560i	$-0.738326\pi$
$263$	−17.3493	+	3.05915i	−1.06980	+	0.188635i	−0.389101	+	0.921195i	$0.627214\pi$
$264$	6.52977	+	2.37664i	0.401880	+	0.146272i
$265$		0			0
$266$	−0.0444853	−	0.0917624i	−0.00272757	−	0.00562632i
$267$		−	28.5410i		−	1.74668i
$268$	−1.31913	+	3.62429i	−0.0805789	+	0.221389i
$269$	0.447725	+	2.53918i	0.0272983	+	0.154816i	0.995410	−	0.0957028i	$-0.0305098\pi$
$269$	0.447725	+	2.53918i	0.0272983	+	0.154816i	−0.968112	+	0.250519i	$0.919399\pi$
$270$		0			0
$271$	−8.49966	+	7.13206i	−0.516318	+	0.433242i	−0.863346	−	0.504613i	$-0.831635\pi$
$271$	−8.49966	+	7.13206i	−0.516318	+	0.433242i	0.347028	+	0.937855i	$0.387191\pi$
$272$	−7.85847	−	1.38566i	−0.476490	−	0.0840180i
$273$	−0.103616	−	0.0598228i	−0.00627113	−	0.00362064i
$274$	−2.98416	−	5.16871i	−0.180280	−	0.312253i
$275$		0			0
$276$	13.5401	−	4.92820i	0.815019	−	0.296643i
$277$	−2.55932	+	1.47762i	−0.153774	+	0.0887817i	−0.574913	−	0.818215i	$-0.694964\pi$
$277$	−2.55932	+	1.47762i	−0.153774	+	0.0887817i	0.421138	+	0.906996i	$0.361631\pi$
$278$	12.1947	+	7.04059i	0.731387	+	0.422266i
$279$	−5.68569	+	32.2452i	−0.340394	+	1.93047i
$280$		0			0
$281$	10.6181	+	8.90966i	0.633424	+	0.531506i	0.901991	−	0.431755i	$-0.142106\pi$
$281$	10.6181	+	8.90966i	0.633424	+	0.531506i	−0.268567	+	0.963261i	$0.586550\pi$
$282$	−13.5386	+	2.38722i	−0.806212	+	0.142157i
$283$	1.58707	−	4.36045i	0.0943418	−	0.259202i	−0.883542	−	0.468353i	$-0.844848\pi$
$283$	1.58707	−	4.36045i	0.0943418	−	0.259202i	0.977883	+	0.209151i	$0.0670699\pi$
$284$	12.8689			0.763627
$285$		0			0
$286$	3.43634			0.203195
$287$	−0.0448316	+	0.123174i	−0.00264632	+	0.00727071i
$288$	−7.23007	+	1.27486i	−0.426036	+	0.0751217i
$289$	−35.7556	−	30.0025i	−2.10327	−	1.76485i
$290$		0			0
$291$	−6.22861	+	35.3242i	−0.365128	+	2.07074i
$292$	1.64682	+	0.950791i	0.0963728	+	0.0556409i
$293$	−10.2765	+	5.93313i	−0.600358	+	0.346617i	−0.769182	−	0.639029i	$-0.779336\pi$
$293$	−10.2765	+	5.93313i	−0.600358	+	0.346617i	0.168824	+	0.985646i	$0.446003\pi$
$294$	−21.1516	+	7.69857i	−1.23359	+	0.448989i
$295$		0			0
$296$	−0.194566	−	0.336998i	−0.0113089	−	0.0195876i
$297$	26.1272	+	15.0846i	1.51606	+	0.875295i
$298$	6.92721	+	1.22145i	0.401282	+	0.0707569i
$299$	5.45851	−	4.58023i	0.315674	−	0.264882i
$300$		0			0
$301$	−0.0394210	−	0.223567i	−0.00227219	−	0.0128862i
$302$	4.81701	−	13.2346i	0.277188	−	0.761567i
$303$		−	59.9670i		−	3.44501i
$304$	−4.34754	−	0.314416i	−0.249349	−	0.0180330i
$305$		0			0
$306$	−55.0508	−	20.0369i	−3.14704	−	1.14543i
$307$	−10.2836	+	1.81328i	−0.586918	+	0.103489i	−0.459218	−	0.888323i	$-0.651870\pi$
$307$	−10.2836	+	1.81328i	−0.586918	+	0.103489i	−0.127699	+	0.991813i	$0.540759\pi$
$308$	−0.0324946	+	0.0387255i	−0.00185155	+	0.00220659i
$309$	8.71060	−	7.30906i	0.495529	−	0.415798i
$310$		0			0
$311$	7.33307	−	12.7012i	0.415820	−	0.720222i	−0.579694	−	0.814834i	$-0.696828\pi$
$311$	7.33307	−	12.7012i	0.415820	−	0.720222i	0.995514	+	0.0946125i	$0.0301612\pi$
$312$	−4.42897	+	2.55706i	−0.250741	+	0.144765i
$313$	−7.34588	−	20.1826i	−0.415214	−	1.14079i	−0.954381	−	0.298592i	$-0.903483\pi$
$313$	−7.34588	−	20.1826i	−0.415214	−	1.14079i	0.539167	−	0.842199i	$-0.318739\pi$
$314$	−2.54495	+	0.926285i	−0.143620	+	0.0522733i
$315$		0			0
$316$	4.75574	−	8.23718i	0.267531	−	0.463378i
$317$	11.6370	+	2.05192i	0.653599	+	0.115247i	0.490608	−	0.871381i	$-0.336775\pi$
$317$	11.6370	+	2.05192i	0.653599	+	0.115247i	0.162991	+	0.986628i	$0.447886\pi$
$318$	7.81812	+	9.31727i	0.438418	+	0.522486i
$319$	−12.5015	−	10.4900i	−0.699950	−	0.587327i
$320$		0			0
$321$	16.9004	+	6.15123i	0.943287	+	0.343328i
$322$			0.104826i			0.00584170i
$323$	−28.7898	−	19.5189i	−1.60191	−	1.08606i
$324$	−22.8744			−1.27080
$325$		0			0
$326$	−2.39569	−	13.5866i	−0.132685	−	0.752493i
$327$	19.4808	−	23.2163i	1.07729	−	1.28386i
$328$	3.60143	+	4.29201i	0.198856	+	0.236987i
$329$	0.0173669	−	0.0984928i	0.000957471	−	0.00543009i
$330$		0			0
$331$	−8.88073	−	15.3819i	−0.488129	−	0.845464i	0.511778	−	0.859118i	$-0.328987\pi$
$331$	−8.88073	−	15.3819i	−0.488129	−	0.845464i	−0.999907	+	0.0136535i	$0.995654\pi$
$332$	0.898948	+	2.46984i	0.0493362	+	0.135550i
$333$	−0.977102	−	2.68456i	−0.0535448	−	0.147113i
$334$	−12.1322	−	21.0137i	−0.663847	−	1.14982i
$335$		0			0
$336$	0.0130644	−	0.0740919i	0.000712721	−	0.00404204i
$337$	1.53351	+	1.82756i	0.0835354	+	0.0995537i	0.806193	−	0.591652i	$-0.201524\pi$
$337$	1.53351	+	1.82756i	0.0835354	+	0.0995537i	−0.722658	+	0.691206i	$0.757080\pi$
$338$	6.73060	−	8.02122i	0.366097	−	0.436297i
$339$	−3.17933	−	18.0309i	−0.172677	−	0.979302i
$340$		0			0
$341$	9.63696			0.521871
$342$	−31.0322	−	7.81574i	−1.67803	−	0.422627i
$343$		−	0.327519i		−	0.0176843i
$344$	−9.11838	−	3.31882i	−0.491630	−	0.178939i
$345$		0			0
$346$	14.8332	+	12.4465i	0.797438	+	0.669130i
$347$	9.89984	+	11.7982i	0.531451	+	0.633359i	0.963249	−	0.268612i	$-0.0865649\pi$
$347$	9.89984	+	11.7982i	0.531451	+	0.633359i	−0.431797	+	0.901971i	$0.642120\pi$
$348$	23.9186	+	4.21749i	1.28217	+	0.226081i
$349$	4.92259	−	8.52618i	0.263500	−	0.456396i	−0.703669	−	0.710528i	$-0.748456\pi$
$349$	4.92259	−	8.52618i	0.263500	−	0.456396i	0.967170	+	0.254132i	$0.0817897\pi$
$350$		0			0
$351$	−20.8645	+	7.59406i	−1.11366	+	0.405341i
$352$	0.739043	+	2.03050i	0.0393911	+	0.108226i
$353$	7.37302	−	4.25682i	0.392426	−	0.226567i	−0.290785	−	0.956789i	$-0.593916\pi$
$353$	7.37302	−	4.25682i	0.392426	−	0.226567i	0.683211	+	0.730221i	$0.260583\pi$
$354$	−5.84218	+	10.1189i	−0.310508	+	0.537816i
$355$		0			0
$356$	6.79876	−	5.70484i	0.360334	−	0.302356i
$357$	0.385899	−	0.459896i	0.0204239	−	0.0243403i
$358$	−8.46188	+	1.49206i	−0.447224	+	0.0788577i
$359$	29.6177	+	10.7800i	1.56317	+	0.568946i	0.971459	−	0.237208i	$-0.0762323\pi$
$359$	29.6177	+	10.7800i	1.56317	+	0.568946i	0.591706	+	0.806154i	$0.298455\pi$
$360$		0			0
$361$	−16.7333	−	8.99976i	−0.880702	−	0.473672i
$362$			4.19496i			0.220482i
$363$	−6.96320	+	19.1312i	−0.365473	+	1.00413i
$364$	−0.00646060	−	0.0366399i	−0.000338628	−	0.00192045i
$365$		0			0
$366$	−28.4329	+	23.8580i	−1.48621	+	1.24708i
$367$	6.86889	+	1.21117i	0.358553	+	0.0632226i	0.350023	−	0.936741i	$-0.386174\pi$
$367$	6.86889	+	1.21117i	0.358553	+	0.0632226i	0.00853004	+	0.999964i	$0.497285\pi$
$368$	3.88037	+	2.24033i	0.202278	+	0.116785i
$369$	20.5669	+	35.6229i	1.07067	+	1.85445i
$370$		0			0
$371$	−0.0831479	+	0.0302634i	−0.00431683	+	0.00157120i
$372$	−12.4207	+	7.17110i	−0.643984	+	0.371804i
$373$	10.4397	+	6.02737i	0.540548	+	0.312085i	0.745301	−	0.666728i	$-0.232306\pi$
$373$	10.4397	+	6.02737i	0.540548	+	0.312085i	−0.204753	+	0.978814i	$0.565639\pi$
$374$	−2.99416	+	16.9807i	−0.154824	+	0.878052i
$375$		0			0
$376$	−3.27478	−	2.74787i	−0.168884	−	0.141710i
$377$	11.8282	−	2.08563i	0.609184	−	0.107416i
$378$	0.111718	−	0.306941i	0.00574613	−	0.0157874i
$379$	6.82285			0.350466			0.175233	−	0.984527i	$-0.443932\pi$
$379$	6.82285			0.350466			0.175233	+	0.984527i	$0.443932\pi$
$380$		0			0
$381$	−27.8978			−1.42925
$382$	−6.45118	+	17.7245i	−0.330071	+	0.906863i
$383$	10.6626	−	1.88011i	0.544834	−	0.0960690i	0.105545	−	0.994415i	$-0.466341\pi$
$383$	10.6626	−	1.88011i	0.544834	−	0.0960690i	0.439290	+	0.898346i	$0.355230\pi$
$384$	−2.46347	−	2.06710i	−0.125714	−	0.105486i
$385$		0			0
$386$	3.08999	−	17.5242i	0.157276	−	0.891958i
$387$	−61.6955	−	35.6199i	−3.13616	−	1.81066i
$388$	−9.65956	+	5.57695i	−0.490390	+	0.283127i
$389$	−7.07236	+	2.57413i	−0.358583	+	0.130513i	−0.515028	−	0.857173i	$-0.672219\pi$
$389$	−7.07236	+	2.57413i	−0.358583	+	0.130513i	0.156446	+	0.987687i	$0.449996\pi$
$390$		0			0
$391$	17.8772	+	30.9642i	0.904088	+	1.56593i
$392$	−6.06170	−	3.49973i	−0.306162	−	0.176763i
$393$	65.7010	+	11.5849i	3.31418	+	0.584379i
$394$	10.3514	−	8.68589i	0.521498	−	0.437589i
$395$		0			0
$396$	2.75473	+	15.6229i	0.138431	+	0.785078i
$397$	−1.69258	+	4.65031i	−0.0849479	+	0.233393i	−0.974892	−	0.222676i	$-0.928521\pi$
$397$	−1.69258	+	4.65031i	−0.0849479	+	0.233393i	0.889944	+	0.456069i	$0.150743\pi$
$398$			7.01614i			0.351687i
$399$	0.184029	−	0.271438i	0.00921299	−	0.0135889i
$400$		0			0
$401$	−18.6833	−	6.80015i	−0.932998	−	0.339583i	−0.169601	−	0.985513i	$-0.554248\pi$
$401$	−18.6833	−	6.80015i	−0.932998	−	0.339583i	−0.763397	+	0.645929i	$0.776470\pi$
$402$	−12.2147	+	2.15378i	−0.609214	+	0.107421i
$403$	−4.55897	+	5.43317i	−0.227099	+	0.270646i
$404$	14.2847	−	11.9863i	0.710692	−	0.596342i
$405$		0			0
$406$	−0.0883457	+	0.153019i	−0.00438452	+	0.00759422i
$407$	−0.728191	+	0.420421i	−0.0360951	+	0.0208395i
$408$	−8.77672	−	24.1138i	−0.434512	−	1.19381i
$409$	12.1132	−	4.40884i	0.598958	−	0.218003i	−0.0247068	−	0.999695i	$-0.507865\pi$
$409$	12.1132	−	4.40884i	0.598958	−	0.218003i	0.623665	+	0.781692i	$0.285643\pi$
$410$		0			0
$411$	9.59657	−	16.6217i	0.473364	−	0.819890i
$412$	3.48218	+	0.614003i	0.171555	+	0.0302497i
$413$	−0.0546391	−	0.0651163i	−0.00268861	−	0.00320416i
$414$	25.1992	+	21.1447i	1.23848	+	1.03920i
$415$		0			0
$416$	−1.49439	−	0.543913i	−0.0732684	−	0.0266675i
$417$			45.2828i			2.21751i
$418$	−0.679394	+	9.39425i	−0.0332303	+	0.459488i
$419$	−4.48425			−0.219070			−0.109535	−	0.993983i	$-0.534936\pi$
$419$	−4.48425			−0.219070			−0.109535	+	0.993983i	$0.534936\pi$
$420$		0			0
$421$	−3.74698	−	21.2502i	−0.182616	−	1.03567i	−0.928980	−	0.370131i	$-0.879313\pi$
$421$	−3.74698	−	21.2502i	−0.182616	−	1.03567i	0.746363	−	0.665539i	$-0.231798\pi$
$422$	4.57505	−	5.45233i	0.222710	−	0.265415i
$423$	−20.1738	−	24.0421i	−0.980882	−	1.16897i
$424$	−0.656766	+	3.72471i	−0.0318954	+	0.180888i
$425$		0			0
$426$	20.6921	+	35.8398i	1.00254	+	1.73644i
$427$	−0.0923527	−	0.253737i	−0.00446926	−	0.0122792i
$428$	1.91279	+	5.25536i	0.0924584	+	0.254027i
$429$	5.52535	+	9.57018i	0.266766	+	0.462053i
$430$		0			0
$431$	2.06827	−	11.7298i	0.0996252	−	0.565003i	−0.893606	−	0.448852i	$-0.851833\pi$
$431$	2.06827	−	11.7298i	0.0996252	−	0.565003i	0.993232	−	0.116151i	$-0.0370557\pi$
$432$	−8.97454	−	10.6954i	−0.431788	−	0.514585i
$433$	14.2251	−	16.9528i	0.683615	−	0.814701i	−0.306952	−	0.951725i	$-0.599309\pi$
$433$	14.2251	−	16.9528i	0.683615	−	0.814701i	0.990568	+	0.137024i	$0.0437537\pi$
$434$	−0.0181183	−	0.102754i	−0.000869706	−	0.00493235i
$435$		0			0
$436$	9.42421			0.451338
$437$	11.4422	+	15.8280i	0.547356	+	0.757156i
$438$			6.11518i			0.292195i
$439$	−6.47904	−	2.35818i	−0.309228	−	0.112550i	0.182745	−	0.983160i	$-0.441502\pi$
$439$	−6.47904	−	2.35818i	−0.309228	−	0.112550i	−0.491973	+	0.870611i	$0.663724\pi$
$440$		0			0
$441$	−39.3649	−	33.0311i	−1.87452	−	1.57291i
$442$	−8.15702	−	9.72116i	−0.387990	−	0.462389i
$443$	1.52212	+	0.268390i	0.0723180	+	0.0127516i	0.209690	−	0.977768i	$-0.432754\pi$
$443$	1.52212	+	0.268390i	0.0723180	+	0.0127516i	−0.137372	+	0.990520i	$0.543866\pi$
$444$	0.625692	−	1.08373i	0.0296940	−	0.0514316i
$445$		0			0
$446$	−4.09711	+	1.49123i	−0.194004	+	0.0706117i
$447$	7.73664	+	21.2562i	0.365931	+	1.00539i
$448$	0.0202608	−	0.0116976i	0.000957231	−	0.000552658i
$449$	2.95993	−	5.12674i	0.139688	−	0.241946i	−0.787691	−	0.616071i	$-0.788724\pi$
$449$	2.95993	−	5.12674i	0.139688	−	0.241946i	0.927378	+	0.374125i	$0.122057\pi$
$450$		0			0
$451$	9.27425	−	7.78202i	0.436708	−	0.366441i
$452$	3.65964	−	4.36139i	0.172135	−	0.205143i
$453$	44.6038	−	7.86485i	2.09567	−	0.369523i
$454$	−8.87656	−	3.23080i	−0.416597	−	0.151629i
$455$		0			0
$456$	−6.11485	−	12.6135i	−0.286354	−	0.590679i
$457$			29.5382i			1.38174i	0.722979	+	0.690870i	$0.242772\pi$
$457$			29.5382i			1.38174i	−0.722979	+	0.690870i	$0.757228\pi$
$458$	7.82113	−	21.4884i	0.365458	−	1.00409i
$459$	−19.3465	−	109.719i	−0.903015	−	5.12125i
$460$		0			0
$461$	23.3287	−	19.5751i	1.08652	−	0.911702i	0.0900776	−	0.995935i	$-0.471288\pi$
$461$	23.3287	−	19.5751i	1.08652	−	0.911702i	0.996446	+	0.0842331i	$0.0268440\pi$
$462$	−0.160099	−	0.0282298i	−0.00744848	−	0.00131337i
$463$	33.6554	+	19.4309i	1.56410	+	0.903033i	0.996835	+	0.0794963i	$0.0253312\pi$
$463$	33.6554	+	19.4309i	1.56410	+	0.903033i	0.567263	+	0.823536i	$0.308002\pi$
$464$	3.77625	+	6.54065i	0.175308	+	0.303642i
$465$		0			0
$466$	−9.93876	+	3.61741i	−0.460404	+	0.167573i
$467$	24.7927	−	14.3141i	1.14727	−	0.662377i	0.199050	−	0.979989i	$-0.436214\pi$
$467$	24.7927	−	14.3141i	1.14727	−	0.662377i	0.948221	+	0.317612i	$0.102881\pi$
$468$	−10.1111	−	5.83766i	−0.467387	−	0.269846i
$469$	0.0156687	−	0.0888615i	0.000723513	−	0.00410324i
$470$		0			0
$471$	−6.67177	−	5.59828i	−0.307419	−	0.257955i
$472$	−3.57818	+	0.630930i	−0.164699	+	0.0290409i
$473$	−7.17136	+	19.7032i	−0.329740	+	0.905952i
$474$	30.5874			1.40492
$475$		0			0
$476$	0.186686			0.00855674
$477$	−9.49693	+	26.0926i	−0.434835	+	1.19470i
$478$	−17.0891	+	3.01327i	−0.781637	+	0.137824i
$479$	12.7889	+	10.7312i	0.584340	+	0.490320i	0.886369	−	0.462979i	$-0.153219\pi$
$479$	12.7889	+	10.7312i	0.584340	+	0.490320i	−0.302029	+	0.953299i	$0.597664\pi$
$480$		0			0
$481$	0.107459	−	0.609433i	0.00489973	−	0.0277877i
$482$	−0.415610	−	0.239953i	−0.0189305	−	0.0109295i
$483$	−0.291939	+	0.168551i	−0.0132837	+	0.00766934i
$484$	−5.94907	+	2.16529i	−0.270412	+	0.0984221i
$485$		0			0
$486$	−15.8373	−	27.4310i	−0.718394	−	1.24430i
$487$	−16.7864	−	9.69165i	−0.760666	−	0.439171i	0.0688690	−	0.997626i	$-0.478061\pi$
$487$	−16.7864	−	9.69165i	−0.760666	−	0.439171i	−0.829535	+	0.558455i	$0.811394\pi$
$488$	−11.3664	−	2.00421i	−0.514534	−	0.0907263i
$489$	33.9866	−	28.5181i	1.53693	−	1.28963i
$490$		0			0
$491$	6.30923	+	35.7814i	0.284731	+	1.61479i	0.706243	+	0.707970i	$0.250389\pi$
$491$	6.30923	+	35.7814i	0.284731	+	1.61479i	−0.421511	+	0.906823i	$0.638500\pi$
$492$	−6.16244	+	16.9312i	−0.277824	+	0.763316i
$493$			60.2666i			2.71427i
$494$	−4.97493	−	4.82719i	−0.223833	−	0.217185i
$495$		0			0
$496$	−4.19091	−	1.52536i	−0.188177	−	0.0684909i
$497$	−0.296495	+	0.0522800i	−0.0132996	+	0.00234508i
$498$	−5.43306	+	6.47487i	−0.243461	+	0.290146i
$499$	5.94585	−	4.98916i	0.266173	−	0.223346i	−0.499926	−	0.866068i	$-0.666640\pi$
$499$	5.94585	−	4.98916i	0.266173	−	0.223346i	0.766099	+	0.642722i	$0.222195\pi$
$500$		0			0
$501$	39.0153	−	67.5765i	1.74308	−	3.01909i
$502$	−5.16548	+	2.98229i	−0.230546	+	0.133106i
$503$	0.217326	+	0.597098i	0.00969008	+	0.0266233i	0.944443	−	0.328674i	$-0.106602\pi$
$503$	0.217326	+	0.597098i	0.00969008	+	0.0266233i	−0.934753	+	0.355297i	$0.884380\pi$
$504$	0.161399	−	0.0587446i	0.00718930	−	0.00261669i
$505$		0			0
$506$	4.84095	−	8.38477i	0.215206	−	0.372748i
$507$	33.1613	+	5.84724i	1.47275	+	0.259685i
$508$	−5.57627	−	6.64554i	−0.247407	−	0.294848i
$509$	−20.1192	−	16.8820i	−0.891767	−	0.748282i	0.0767966	−	0.997047i	$-0.475531\pi$
$509$	−20.1192	−	16.8820i	−0.891767	−	0.748282i	−0.968564	+	0.248765i	$0.919975\pi$
$510$		0			0
$511$	−0.0418048	−	0.0152157i	−0.00184934	−	0.000673103i
$512$		−	1.00000i		−	0.0441942i
$513$	−16.6355	−	58.5408i	−0.734476	−	2.58464i
$514$	−13.5279			−0.596692
$515$		0			0
$516$	−5.41871	−	30.7311i	−0.238546	−	1.35286i
$517$	−5.93764	+	7.07620i	−0.261137	+	0.311211i
$518$	0.00585180	+	0.00697390i	0.000257113	+	0.000306416i
$519$	−10.8130	+	61.3235i	−0.474637	+	2.69180i
$520$		0			0
$521$	−20.1453	−	34.8927i	−0.882583	−	1.52868i	−0.848459	−	0.529262i	$-0.822469\pi$
$521$	−20.1453	−	34.8927i	−0.882583	−	1.52868i	−0.0341245	−	0.999418i	$-0.510864\pi$
$522$	18.9641	+	52.1035i	0.830038	+	2.28051i
$523$	5.72897	+	15.7402i	0.250510	+	0.688271i	0.999665	+	0.0258764i	$0.00823762\pi$
$523$	5.72897	+	15.7402i	0.250510	+	0.688271i	−0.749155	+	0.662395i	$0.769540\pi$
$524$	10.3728	+	17.9662i	0.453138	+	0.784859i
$525$		0			0
$526$	3.05915	−	17.3493i	0.133385	−	0.756466i
$527$	−22.8758	−	27.2623i	−0.996485	−	1.18756i
$528$	−4.46663	+	5.32312i	−0.194385	+	0.231659i
$529$	0.507688	+	2.87924i	0.0220734	+	0.125184i
$530$		0			0
$531$	−26.6748			−1.15759
$532$	0.101443	−	0.0104179i	0.00439813	−	0.000451675i
$533$			8.91014i			0.385941i
$534$	26.8198	+	9.76161i	1.16061	+	0.422426i
$535$		0			0
$536$	−2.95455	−	2.47916i	−0.127617	−	0.107083i
$537$	−17.7614	−	21.1672i	−0.766461	−	0.913432i
$538$	−2.53918	−	0.447725i	−0.109472	−	0.0193028i
$539$	−7.56227	+	13.0982i	−0.325730	+	0.564181i
$540$		0			0
$541$	−28.7784	+	10.4745i	−1.23728	+	0.450334i	−0.876085	−	0.482156i	$-0.839854\pi$
$541$	−28.7784	+	10.4745i	−1.23728	+	0.450334i	−0.361196	+	0.932490i	$0.617632\pi$
$542$	−3.79489	−	10.4264i	−0.163005	−	0.447851i
$543$	−11.6830	+	6.74515i	−0.501363	+	0.289462i
$544$	3.98985	−	6.91062i	0.171063	−	0.296291i
$545$		0			0
$546$	0.0916539	−	0.0769067i	0.00392242	−	0.00329130i
$547$	0.00515474	−	0.00614318i	0.000220401	−	0.000262663i	−0.765934	−	0.642919i	$-0.777723\pi$
$547$	0.00515474	−	0.00614318i	0.000220401	−	0.000262663i	0.766155	+	0.642656i	$0.222168\pi$
$548$	5.87764	−	1.03639i	0.251081	−	0.0442723i
$549$	−79.6251	−	28.9812i	−3.39831	−	1.23689i
$550$		0			0
$551$	3.36316	+	32.7483i	0.143275	+	1.39512i
$552$			14.4091i			0.613291i
$553$	−0.0761070	+	0.209102i	−0.00323640	+	0.00889194i
$554$	−0.513173	−	2.91035i	−0.0218026	−	0.123649i
$555$		0			0
$556$	−10.7868	+	9.05120i	−0.457462	+	0.383856i
$557$	6.59116	+	1.16220i	0.279276	+	0.0492440i	0.311532	−	0.950236i	$-0.399158\pi$
$557$	6.59116	+	1.16220i	0.279276	+	0.0492440i	−0.0322555	+	0.999480i	$0.510269\pi$
$558$	−28.3559	−	16.3713i	−1.20040	−	0.693052i
$559$	−7.71578	−	13.3641i	−0.326343	−	0.565242i
$560$		0			0
$561$	−52.1056	+	18.9649i	−2.19990	+	0.800698i
$562$	−12.0040	+	6.93049i	−0.506356	+	0.292345i
$563$	5.72191	+	3.30354i	0.241150	+	0.139228i	0.615705	−	0.787977i	$-0.288871\pi$
$563$	5.72191	+	3.30354i	0.241150	+	0.139228i	−0.374555	+	0.927205i	$0.622205\pi$
$564$	2.38722	−	13.5386i	0.100520	−	0.570078i
$565$		0			0
$566$	3.55467	+	2.98272i	0.149414	+	0.125373i
$567$	0.527019	−	0.0929276i	0.0221327	−	0.00390259i
$568$	−4.40141	+	12.0928i	−0.184679	+	0.507402i
$569$	18.2452			0.764879			0.382440	−	0.923980i	$-0.375084\pi$
$569$	18.2452			0.764879			0.382440	+	0.923980i	$0.375084\pi$
$570$		0			0
$571$	−4.61851			−0.193279			−0.0966393	−	0.995319i	$-0.530809\pi$
$571$	−4.61851			−0.193279			−0.0966393	+	0.995319i	$0.530809\pi$
$572$	−1.17530	+	3.22910i	−0.0491416	+	0.135015i
$573$	−59.7356	+	10.5330i	−2.49549	+	0.440022i
$574$	−0.100412	−	0.0842558i	−0.00419112	−	0.00351677i
$575$		0			0
$576$	1.27486	−	7.23007i	0.0531190	−	0.301253i
$577$	34.9245	+	20.1637i	1.45393	+	0.839424i	0.998701	−	0.0509529i	$-0.0162258\pi$
$577$	34.9245	+	20.1637i	1.45393	+	0.839424i	0.455224	+	0.890377i	$0.349559\pi$
$578$	40.4223	−	23.3378i	1.68135	−	0.970725i
$579$	53.7733	−	19.5719i	2.23474	−	0.813379i
$580$		0			0
$581$	−0.0307453	−	0.0532524i	−0.00127553	−	0.00220928i
$582$	−31.0636	−	17.9346i	−1.28763	−	0.743412i
$583$	8.04841	+	1.41915i	0.333331	+	0.0587752i
$584$	−1.45670	+	1.22231i	−0.0602785	+	0.0505797i
$585$		0			0
$586$	−2.06055	−	11.6860i	−0.0851207	−	0.482743i
$587$	5.21623	−	14.3315i	0.215297	−	0.591523i	−0.784286	−	0.620399i	$-0.786971\pi$
$587$	5.21623	−	14.3315i	0.215297	−	0.591523i	0.999583	+	0.0288761i	$0.00919283\pi$
$588$		−	22.5091i		−	0.928260i
$589$	−13.9518	−	13.5375i	−0.574876	−	0.557803i
$590$		0			0
$591$	40.8344	+	14.8625i	1.67970	+	0.611363i
$592$	0.383220	−	0.0675720i	0.0157502	−	0.00277719i
$593$	−25.7487	+	30.6860i	−1.05737	+	1.26012i	−0.0929726	+	0.995669i	$0.529637\pi$
$593$	−25.7487	+	30.6860i	−1.05737	+	1.26012i	−0.964398	+	0.264456i	$0.914808\pi$
$594$	−23.1109	+	19.3923i	−0.948251	+	0.795677i
$595$		0			0
$596$	−3.51704	+	6.09168i	−0.144063	+	0.249525i
$597$	−19.5399	+	11.2814i	−0.799716	+	0.461716i
$598$	2.43709	+	6.69585i	0.0996600	+	0.273814i
$599$	−25.5138	+	9.28628i	−1.04247	+	0.379427i	−0.805815	−	0.592167i	$-0.798272\pi$
$599$	−25.5138	+	9.28628i	−1.04247	+	0.379427i	−0.236652	+	0.971594i	$0.576050\pi$
$600$		0			0
$601$	12.9663	−	22.4583i	0.528907	−	0.916094i	−0.470525	−	0.882387i	$-0.655935\pi$
$601$	12.9663	−	22.4583i	0.528907	−	0.916094i	0.999432	−	0.0337070i	$-0.0107313\pi$
$602$	0.223567	+	0.0394210i	0.00911193	+	0.00160668i
$603$	−18.2010	−	21.6911i	−0.741203	−	0.883332i
$604$	10.7890	+	9.05302i	0.438997	+	0.368362i
$605$		0			0
$606$	56.3506	+	20.5099i	2.28908	+	0.833159i
$607$		−	15.2583i		−	0.619316i	−0.950848	−	0.309658i	$-0.899785\pi$
$607$		−	15.2583i		−	0.619316i	0.950848	−	0.309658i	$-0.100215\pi$
$608$	1.78240	−	3.97782i	0.0722859	−	0.161322i
$609$	−0.568211			−0.0230251
$610$		0			0
$611$	−1.18053	−	6.69510i	−0.0477590	−	0.270855i
$612$	37.6570	−	44.8778i	1.52219	−	1.81408i
$613$	3.03440	+	3.61626i	0.122558	+	0.146059i	0.823835	−	0.566830i	$-0.191831\pi$
$613$	3.03440	+	3.61626i	0.122558	+	0.146059i	−0.701276	+	0.712890i	$0.747386\pi$
$614$	1.81328	−	10.2836i	0.0731781	−	0.415013i
$615$		0			0
$616$	−0.0252763	−	0.0437798i	−0.00101841	−	0.00176394i
$617$	−10.3569	−	28.4553i	−0.416953	−	1.14557i	−0.953420	−	0.301647i	$-0.902463\pi$
$617$	−10.3569	−	28.4553i	−0.416953	−	1.14557i	0.536467	−	0.843922i	$-0.319759\pi$
$618$	3.88907	+	10.6851i	0.156441	+	0.429819i
$619$	−2.84795	−	4.93279i	−0.114469	−	0.198266i	0.803099	−	0.595846i	$-0.203183\pi$
$619$	−2.84795	−	4.93279i	−0.114469	−	0.198266i	−0.917567	+	0.397581i	$0.869850\pi$
$620$		0			0
$621$	−10.8632	+	61.6082i	−0.435925	+	2.47225i
$622$	9.42721	+	11.2349i	0.377997	+	0.450479i
$623$	−0.133465	+	0.159058i	−0.00534718	+	0.00637252i
$624$	−0.888059	−	5.03643i	−0.0355508	−	0.201619i
$625$		0			0
$626$	21.4779			0.858430
$627$	−27.2554	+	13.2131i	−1.08847	+	0.527679i
$628$		−	2.70828i		−	0.108072i
$629$	2.91789	+	1.06203i	0.116344	+	0.0423457i
$630$		0			0
$631$	−32.4485	−	27.2275i	−1.29175	−	1.08391i	−0.991508	−	0.130048i	$-0.958487\pi$
$631$	−32.4485	−	27.2275i	−1.29175	−	1.08391i	−0.300246	−	0.953862i	$-0.597069\pi$
$632$	6.11386	+	7.28621i	0.243196	+	0.289830i
$633$	22.5410	+	3.97459i	0.895925	+	0.157976i
$634$	−5.90826	+	10.2334i	−0.234647	+	0.406420i
$635$		0			0
$636$	−11.4293	+	4.15993i	−0.453202	+	0.164952i
$637$	−3.80709	−	10.4599i	−0.150842	−	0.414436i
$638$	14.1331	−	8.15977i	0.559537	−	0.323049i
$639$	−47.2391	+	81.8206i	−1.86875	+	3.23677i
$640$		0			0
$641$	−20.8636	+	17.5066i	−0.824062	+	0.691470i	−0.953920	−	0.300063i	$-0.902992\pi$
$641$	−20.8636	+	17.5066i	−0.824062	+	0.691470i	0.129858	+	0.991533i	$0.458548\pi$
$642$	−11.5605	+	13.7773i	−0.456258	+	0.543747i
$643$	−3.45211	+	0.608700i	−0.136138	+	0.0240048i	−0.241302	−	0.970450i	$-0.577574\pi$
$643$	−3.45211	+	0.608700i	−0.136138	+	0.0240048i	0.105164	+	0.994455i	$0.466463\pi$
$644$	−0.0985039	−	0.0358525i	−0.00388160	−	0.00141279i
$645$		0			0
$646$	28.1884	−	20.3777i	1.10906	−	0.801750i
$647$			44.9855i			1.76856i	0.466956	+	0.884280i	$0.345351\pi$
$647$			44.9855i			1.76856i	−0.466956	+	0.884280i	$0.654649\pi$
$648$	7.82350	−	21.4949i	0.307336	−	0.844399i
$649$	1.36332	+	7.73179i	0.0535151	+	0.303499i
$650$		0			0
$651$	0.257037	−	0.215679i	0.0100741	−	0.00845314i
$652$	13.5866	+	2.39569i	0.532093	+	0.0938223i
$653$	13.7877	+	7.96033i	0.539555	+	0.311512i	0.744898	−	0.667178i	$-0.232498\pi$
$653$	13.7877	+	7.96033i	0.539555	+	0.311512i	−0.205344	+	0.978690i	$0.565831\pi$
$654$	15.1534	+	26.2464i	0.592543	+	1.02632i
$655$		0			0
$656$	−5.26493	+	1.91628i	−0.205561	+	0.0748181i
$657$	−12.0903	+	6.98034i	−0.471687	+	0.272329i
$658$	0.0866132	+	0.0500061i	0.00337653	+	0.00194944i
$659$	−3.30453	+	18.7409i	−0.128726	+	0.730042i	0.850299	+	0.526301i	$0.176421\pi$
$659$	−3.30453	+	18.7409i	−0.128726	+	0.730042i	−0.979025	+	0.203741i	$0.934690\pi$
$660$		0			0
$661$	17.6520	+	14.8118i	0.686583	+	0.576111i	0.917922	−	0.396762i	$-0.129866\pi$
$661$	17.6520	+	14.8118i	0.686583	+	0.576111i	−0.231339	+	0.972873i	$0.574311\pi$
$662$	17.4916	−	3.08425i	0.679831	−	0.119873i
$663$	13.9576	−	38.3481i	0.542067	−	1.48932i
$664$	−2.62835			−0.102000
$665$		0			0
$666$	2.85685			0.110701
$667$	11.5740	−	31.7994i	0.448148	−	1.23128i
$668$	23.8958	−	4.21348i	0.924558	−	0.163025i
$669$	−10.7409	−	9.01268i	−0.415267	−	0.348450i
$670$		0			0
$671$	−4.33073	+	24.5608i	−0.167186	+	0.948158i
$672$	0.0651553	+	0.0376174i	0.00251342	+	0.00145112i
$673$	−9.85260	+	5.68840i	−0.379790	+	0.219272i	−0.677727	−	0.735314i	$-0.737035\pi$
$673$	−9.85260	+	5.68840i	−0.379790	+	0.219272i	0.297937	+	0.954586i	$0.403701\pi$
$674$	−2.24184	+	0.815962i	−0.0863523	+	0.0314297i
$675$		0			0
$676$	5.23548	+	9.06812i	0.201365	+	0.348774i
$677$	−36.1782	−	20.8875i	−1.39044	−	0.802771i	−0.397076	−	0.917786i	$-0.629975\pi$
$677$	−36.1782	−	20.8875i	−1.39044	−	0.802771i	−0.993364	+	0.115015i	$0.963308\pi$
$678$	18.0309	+	3.17933i	0.692471	+	0.122101i
$679$	0.199897	−	0.167733i	0.00767134	−	0.00643701i
$680$		0			0
$681$	−5.27501	−	29.9160i	−0.202139	−	1.14639i
$682$	−3.29603	+	9.05578i	−0.126212	+	0.346764i
$683$		−	9.65205i		−	0.369325i	−0.982802	−	0.184663i	$-0.940881\pi$
$683$		−	9.65205i		−	0.369325i	0.982802	−	0.184663i	$-0.0591193\pi$
$684$	17.9580	−	26.4876i	0.686643	−	1.01278i
$685$		0			0
$686$	0.307767	+	0.112018i	0.0117506	+	0.00427687i
$687$	72.4208	−	12.7697i	2.76303	−	0.487196i
$688$	6.23734	−	7.43337i	0.237796	−	0.283395i
$689$	−4.60757	+	3.86621i	−0.175535	+	0.147291i
$690$		0			0
$691$	3.58223	−	6.20461i	0.136275	−	0.236034i	−0.789809	−	0.613353i	$-0.789820\pi$
$691$	3.58223	−	6.20461i	0.136275	−	0.236034i	0.926084	+	0.377318i	$0.123154\pi$
$692$	−16.7692	+	9.68169i	−0.637469	+	0.368043i
$693$	−0.126936	−	0.348755i	−0.00482191	−	0.0132481i
$694$	−14.4726	+	5.26759i	−0.549372	+	0.199955i
$695$		0			0
$696$	−12.1438	+	21.0337i	−0.460309	+	0.797279i
$697$	−44.0296	−	7.76361i	−1.66774	−	0.294068i
$698$	6.32836	+	7.54185i	0.239532	+	0.285463i
$699$	−26.0552	−	21.8629i	−0.985498	−	0.826931i
$700$		0			0
$701$	−5.58820	−	2.03394i	−0.211063	−	0.0768208i	0.234325	−	0.972158i	$-0.424712\pi$
$701$	−5.58820	−	2.03394i	−0.211063	−	0.0768208i	−0.445388	+	0.895338i	$0.646934\pi$
$702$		−	22.2035i		−	0.838019i
$703$	1.64482	+	0.414263i	0.0620356	+	0.0156242i
$704$	−2.16082			−0.0814389
$705$		0			0
$706$	1.47838	+	8.38429i	0.0556394	+	0.315547i
$707$	−0.280421	+	0.334193i	−0.0105463	+	0.0125686i
$708$	−7.51056	−	8.95073i	−0.282264	−	0.336389i
$709$	−6.60131	+	37.4379i	−0.247918	+	1.40601i	0.565701	+	0.824611i	$0.308606\pi$
$709$	−6.60131	+	37.4379i	−0.247918	+	1.40601i	−0.813618	+	0.581400i	$0.802505\pi$
$710$		0			0
$711$	34.9148	+	60.4742i	1.30941	+	2.26796i
$712$	3.03548	+	8.33992i	0.113759	+	0.312552i
$713$	6.83465	+	18.7780i	0.255959	+	0.703243i
$714$	0.300176	+	0.519920i	0.0112338	+	0.0194575i
$715$		0			0
$716$	1.49206	−	8.46188i	0.0557608	−	0.316235i
$717$	−35.8698	−	42.7480i	−1.33958	−	1.59645i
$718$	−20.2597	+	24.1446i	−0.756087	+	0.901069i
$719$	−1.48425	−	8.41760i	−0.0553532	−	0.313923i	0.944542	−	0.328390i	$-0.106506\pi$
$719$	−1.48425	−	8.41760i	−0.0553532	−	0.313923i	−0.999895	+	0.0144667i	$0.995395\pi$
$720$		0			0
$721$	−0.0827228			−0.00308076
$722$	14.1801	−	12.6461i	0.527730	−	0.470639i
$723$		−	1.54330i		−	0.0573958i
$724$	−3.94197	−	1.43476i	−0.146502	−	0.0533225i
$725$		0			0
$726$	−15.5959	−	13.0865i	−0.578819	−	0.485687i
$727$	5.38809	+	6.42127i	0.199833	+	0.238152i	0.856650	−	0.515899i	$-0.172542\pi$
$727$	5.38809	+	6.42127i	0.199833	+	0.238152i	−0.656817	+	0.754050i	$0.728097\pi$
$728$	0.0366399	+	0.00646060i	0.00135796	+	0.000239446i
$729$	16.6186	−	28.7842i	0.615503	−	1.06608i
$730$		0			0
$731$	72.7620	−	26.4832i	2.69120	−	0.979516i
$732$	−12.6946	−	34.8781i	−0.469205	−	1.28913i
$733$	10.3264	−	5.96195i	0.381414	−	0.220210i	−0.297019	−	0.954872i	$-0.595993\pi$
$733$	10.3264	−	5.96195i	0.381414	−	0.220210i	0.678433	+	0.734662i	$0.262659\pi$
$734$	−3.48743	+	6.04040i	−0.128723	+	0.222955i
$735$		0			0
$736$	−3.43239	+	2.88011i	−0.126519	+	0.106162i
$737$	−5.35701	+	6.38424i	−0.197328	+	0.235166i
$738$	−40.5088	+	7.14280i	−1.49115	+	0.262930i
$739$	23.9241	+	8.70767i	0.880063	+	0.320317i	0.742235	−	0.670140i	$-0.233766\pi$
$739$	23.9241	+	8.70767i	0.880063	+	0.320317i	0.137828	+	0.990456i	$0.455988\pi$
$740$		0			0
$741$	5.44441	−	21.6169i	0.200005	−	0.794117i
$742$		−	0.0884842i		−	0.00324836i
$743$	−5.45769	+	14.9949i	−0.200223	+	0.550109i	−0.998648	−	0.0519860i	$-0.983445\pi$
$743$	−5.45769	+	14.9949i	−0.200223	+	0.550109i	0.798425	+	0.602095i	$0.205667\pi$
$744$	−2.49050	−	14.1243i	−0.0913061	−	0.517823i
$745$		0			0
$746$	−9.23447	+	7.74864i	−0.338098	+	0.283698i
$747$	−19.0032	−	3.35077i	−0.695289	−	0.122598i
$748$	−14.9326	−	8.62134i	−0.545990	−	0.315227i
$749$	−0.0654201	−	0.113311i	−0.00239040	−	0.00414029i
$750$		0			0
$751$	1.48505	−	0.540514i	0.0541903	−	0.0197237i	−0.314783	−	0.949164i	$-0.601932\pi$
$751$	1.48505	−	0.540514i	0.0541903	−	0.0197237i	0.368973	+	0.929440i	$0.379709\pi$
$752$	3.70219	−	2.13746i	0.135005	−	0.0779452i
$753$	−16.6113	−	9.59055i	−0.605350	−	0.349499i
$754$	−2.08563	+	11.8282i	−0.0759543	+	0.430758i
$755$		0			0
$756$	0.250221	+	0.209960i	0.00910045	+	0.00763618i
$757$	18.9354	−	3.33882i	0.688217	−	0.121351i	0.181406	−	0.983408i	$-0.441935\pi$
$757$	18.9354	−	3.33882i	0.688217	−	0.121351i	0.506811	+	0.862057i	$0.330824\pi$
$758$	−2.33355	+	6.41138i	−0.0847584	+	0.232872i
$759$	31.1354			1.13014
$760$		0			0
$761$	12.6228			0.457576			0.228788	−	0.973476i	$-0.426524\pi$
$761$	12.6228			0.457576			0.228788	+	0.973476i	$0.426524\pi$
$762$	9.54161	−	26.2154i	0.345656	−	0.949683i
$763$	−0.217131	+	0.0382860i	−0.00786067	+	0.00138605i
$764$	−14.4491	−	12.1243i	−0.522751	−	0.438640i
$765$		0			0
$766$	−1.88011	+	10.6626i	−0.0679310	+	0.385256i
$767$	−5.00402	−	2.88907i	−0.180685	−	0.104318i
$768$	2.78500	−	1.60792i	0.100495	−	0.0580208i
$769$	−37.7534	+	13.7411i	−1.36142	+	0.495518i	−0.916494	−	0.400048i	$-0.868993\pi$
$769$	−37.7534	+	13.7411i	−1.36142	+	0.495518i	−0.444929	+	0.895566i	$0.646771\pi$
$770$		0			0
$771$	−21.7518	−	37.6753i	−0.783373	−	1.35684i
$772$	15.4105	+	8.89727i	0.554637	+	0.320220i
$773$	−25.4287	−	4.48376i	−0.914606	−	0.161270i	−0.303512	−	0.952828i	$-0.598159\pi$
$773$	−25.4287	−	4.48376i	−0.914606	−	0.161270i	−0.611094	+	0.791558i	$0.709270\pi$
$774$	54.5729	−	45.7921i	1.96158	−	1.64596i
$775$		0			0
$776$	−1.93685	−	10.9844i	−0.0695290	−	0.394319i
$777$	−0.0100131	+	0.0275107i	−0.000359217	+	0.000986941i
$778$		−	7.52625i		−	0.269829i
$779$	−24.3585	−	1.76162i	−0.872735	−	0.0631164i
$780$		0			0
$781$	26.1303	+	9.51065i	0.935016	+	0.340318i
$782$	−35.2112	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-3.16698 + 0.558424i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.558424 - 3.16698i) q^{6} +(0.0202608 + 0.0116976i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.89886 - 2.51098i) q^{9} +O(q^{10})\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-3.16698 + 0.558424i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.558424 - 3.16698i) q^{6} +(0.0202608 + 0.0116976i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.89886 - 2.51098i) q^{9} +(-1.08041 - 1.87132i) q^{11} +(2.78500 + 1.60792i) q^{12} +(1.56613 + 0.276152i) q^{13} +(-0.0179217 + 0.0150381i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-2.72922 + 7.49847i) q^{17} +7.34161i q^{18} +(-1.06458 + 4.22690i) q^{19} +(-0.0706976 - 0.0257318i) q^{21} +(2.12799 - 0.375222i) q^{22} +(2.88011 - 3.43239i) q^{23} +(-2.46347 + 2.06710i) q^{24} +(-0.795147 + 1.37724i) q^{26} +(-12.0914 + 6.98095i) q^{27} +(-0.00800160 - 0.0219842i) q^{28} +(7.09702 - 2.58310i) q^{29} +(-2.22993 + 3.86236i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(4.46663 + 5.32312i) q^{33} +(-6.11281 - 5.12925i) q^{34} +(-6.89886 - 2.51098i) q^{36} -0.389132i q^{37} +(-3.60788 - 2.44606i) q^{38} -5.11413 q^{39} +(0.972920 + 5.51771i) q^{41} +(0.0483600 - 0.0576332i) q^{42} +(-6.23734 - 7.43337i) q^{43} +(-0.375222 + 2.12799i) q^{44} +(2.24033 + 3.88037i) q^{46} +(-1.46211 - 4.01711i) q^{47} +(-1.09988 - 3.02190i) q^{48} +(-3.49973 - 6.06170i) q^{49} +(4.45606 - 25.2716i) q^{51} +(-1.02222 - 1.21824i) q^{52} +(-2.43113 + 2.89731i) q^{53} +(-2.42446 - 13.7498i) q^{54} +0.0233951 q^{56} +(1.01111 - 13.9810i) q^{57} +7.55249i q^{58} +(-3.41426 - 1.24269i) q^{59} +(-8.84152 - 7.41891i) q^{61} +(-2.86675 - 3.41646i) q^{62} +(0.169148 + 0.0298254i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.52977 + 2.37664i) q^{66} +(-1.31913 - 3.62429i) q^{67} +(6.91062 - 3.98985i) q^{68} +(-7.20454 + 12.4786i) q^{69} +(-9.85813 + 8.27195i) q^{71} +(4.71909 - 5.62400i) q^{72} +(-1.87269 + 0.330206i) q^{73} +(0.365664 + 0.133091i) q^{74} +(3.53251 - 2.55369i) q^{76} -0.0505526i q^{77} +(1.74914 - 4.80571i) q^{78} +(1.65165 + 9.36698i) q^{79} +(17.5228 - 14.7034i) q^{81} +(-5.51771 - 0.972920i) q^{82} +(-2.27622 - 1.31417i) q^{83} +(0.0376174 + 0.0651553i) q^{84} +(9.11838 - 3.31882i) q^{86} +(-21.0337 + 12.1438i) q^{87} +(-1.87132 - 1.08041i) q^{88} +(-1.54115 + 8.74032i) q^{89} +(0.0285008 + 0.0239150i) q^{91} +(-4.41259 + 0.778059i) q^{92} +(4.90532 - 13.4773i) q^{93} +4.27492 q^{94} +3.21584 q^{96} +(3.81486 - 10.4812i) q^{97} +(6.89312 - 1.21544i) q^{98} +(-12.1524 - 10.1971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36q + 36q^{9} + O(q^{10}) \)	\( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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